I don't know of any evidence for the use of woad during the Viking Age. The closest thing I've come across is the report of a 10c Spanish traveler to Denmark who thought that the eyeliner used there made people look more attractive. There's also the 10c account of Ibn Fadlan, a traveler from Baghdad who seems to say that the Norse speakers in Russia tattooed themselves.

By and large, I've been pleased with the costuming and such that I've seen on the television series The Last Kingdom, although I must admit I haven't scrutinized it too carefully. My biggest complaint is that they oversimplify the contrast of Danish=pagan vs. English=Christian. This probably aptly represents the perspective of Alfred's court, or at least the superhero image of Alfred that his court was trying to promote, but things were probably much more shady in most of Britain, particularly the north.

An important part of (modern) Scotland had actually belonged to the Anglo-Saxon kingdom of Northumbria. Northumbria had been cobbled together a few centuries before from at least two earlier kingdoms, and the Northumbrian elites had converted early to Christianity. They adopted a lot of their church organization and monastic habits from the Irish, whom they confusingly called Scots. Perhaps because of the wealth that the Northumbrian church was able to amass, they became early victims of viking raiders. The early attack on Lindisfarne in 793 seems to have been well known, and there was also a monastery devastated at Portmahomack, apparently by Norse raiders. Although Norse raiders eventually took over political control of Northumbria, they actually left much of the church intact, allowing the archbishops of York to continue minting and sometimes even minting coins with them.

Based on linguistic evidence (mapping where Norse words got used as parts of place names), it looks like Norse influence was slow to move from east to west across mainland Scotland. And based on the Norse referring to the north tip of Scotland as Sutherland or the 'Southern Land', it seems like Norse influence from Orkney (where people could rightly think of themselves as being at the center of the world) never extended far south. In the Hebrides, however, the situation was markedly different. The Hebrides were effectively part of the Norse highway linking Irish Sea settlements like Dublin to Orkney and then out into the wider Norse world. Evidence is patchy, but I suspect that settlement from Scandinavia was limited, but that the indigenous people took on Norse identities.

So what about the people who were non-Norsified? I'd be very hesitant to read too much into the word 'Pict' during this period. There was certainly some sort of non-Norse, non-Anglo-Saxon identity at work on the Scottish mainland outside of old Northumbria, but they didn't leave many records. Modern scholars who use the word 'Pictish' during this period are most likely referring to art styles rather than people. Martin Carver's Portmahomack: Monastery of the Picts is the best review I've seen, and there's a short article summarizing much of his research free online.

So this was actually a really exciting time to be from Scotland, a time of opportunity and experiment, albeit one also of violence. And certainly, there were cosmopolitan crews sailing the Viking world. The crew who were executed at Ridgeway Hill in Dorset gave archaeologists a unique opportunity to identify the far-ranging origins of the young men who made up a raiding group.

Anyways, that goes pretty far from your original question, but I wanted to do better than a simple answer of 'no'. It looks like you've got a pretty good group going. As an added bonus, one of my favorite references for reenacting is the cookbook, An Early Meal. Keep up the good work keeping history alive!